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Chapter 1: Problem 41

In Exercises \(1-72\), compute the value of each expression. $$3-6+1-(-4)$$

Short Answer

Expert verified
The value of the expression is 2.

Step by step solution

01

Simplify within the parentheses

First, simplify the expression inside the parentheses: -4 remains -4.
02

Apply the negative sign to -4

Next, change the double negative. -(-4) becomes +4.
03

Evaluate the expression

Combine all terms from left to right: 3 - 6 + 1 + 4.
04

Perform the subtraction

Start by performing the operation 3-6: 3 - 6 = -3.
05

Add remaining values

Now add the remaining terms to -3: -3 + 1 + 4.
06

Simplify further

First, add -3 and 1: -3 + 1 = -2.
07

Final addition

Finally, add -2 and 4: -2 + 4 = 2.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Order of Operations
Understanding the correct sequence in which to solve parts of an arithmetic expression is crucial. This is referred to as the 'order of operations'. In math, we use the acronym PEMDAS to remember this order:
  • **P**arentheses
  • **E**xponents
  • **M**ultiplication and **D**ivision (left to right)
  • **A**ddition and **S**ubtraction (left to right)
In the given exercise, order of operations dictates that we first handle parentheses. We also see addition and subtraction from left to right.

Following the order of operations ensures that we get the correct result.
Negative Numbers
Negative numbers can sometimes be confusing, especially when dealing with operations involving multiple negative signs. A negative number is any number less than zero.

Let's examine this further:
  • A single minus sign means you are 'taking away'. Example: -4 means 'negative four'.
  • To subtract a negative number, change it into addition. Example: -(-4) becomes +4.
So in the expression \( 3-6+1-(-4) \), we turn \( -(-4) \) into \( +4 \).
This makes the expression easier to compute.
Arithmetic Operations
Arithmetic operations include addition, subtraction, multiplication, and division. Each of these operations follows specific rules and affects the numbers differently.

In our example exercise: \( 3-6+1-(-4) \), the steps to solve it involve:
  • Adding and subtracting numbers from left to right after handling parentheses.
  • First, compute \( 3-6 \), which equals \( -3 \).
  • Next, add \( 1 \): \( -3 + 1 = -2 \).
  • Finally, add \( 4 \): \( -2 + 4 = 2 \).
Mastery of these arithmetic operations is essential for solving more complex algebra problems.

Practicing these operations can help you become more comfortable in working with different expressions.

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Most popular questions from this chapter

Evaluate the given expression. Remember to follow the order of operations. $$4+\\{3+5[2+2(3+1)]\\}$$

Evaluate the given expression. Remember to follow the order of operations. $$18+2 \cdot 9+5$$

Explain how you could use the commutative and/or associative properties to make the following computations easier to do. (a) \(-1.7+12.9-8.3\) (b) 10( 7)\((-2.3)\) (c) \(\frac{-10(3.2)}{-1.6}\) (d) \(-30\left(\frac{1.6}{3}\right)(-10)\)

In Exercises \(1-72\), compute the value of each expression. $$-561-412-(-678)$$

Evaluate the given expression. Remember to follow the order of operations. $$\frac{15+2 \cdot 3}{3+2 \cdot 2}$$
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